The high-velocity Ly(Alpha) emission from SN 1987A observed with the Space Telescope Imaging Spectrograph (STIS) evidently comes from a reverse shock formed where the outer envelope of SN 1987A strikes ionized gas inside the inner circumstellar ring. The observations can be explained by a simple kinematic model, in which the Ly(Alpha) emission comes from hydrogen atoms with radial velocity approximately 15,000 km s(exp -1) crossing a reverse shock in the shape of a slightly prolate ellipsoid with equatorial radius 4.8 x 10(exp 17) cm or approximately 80% of the distance to the inner surface of the inner ring. N v double Lambda 1239, 1243 emission, if present, has a net luminosity approximately less than 30% times that of the Ly(Alpha) emission. Future STIS observations should enable us to predict the time of impact with the inner ring and to determine unambiguously whether or not N v emission is present. These observations will offer a unique opportunity to probe the structure of SN 1987A's circumstellar environment and the hydrodynamics and kinetics of very fast shocks.